A way to ripple the fabric of space?

So i was sitting in Algebra the other day, day-dreaming when i thought of something:

I know gravity exists because all objects have mass that bend space causing a trampoline effect and pull objects towards them. So, what happens if you have something that has extreme mass (say a large star) and make it dissapear (yes, i know you cannot create/destroy matter, its an example.). It would then make the fabric of space stretch or "bungee" back to its original flat position. But what if you made it reappear shortly or immediatly after? and what if you did this rapidly? would it create a wave effect through the fabric of space or would it just snap back flat without any "hill"(~) effect? And if it does ripple space what would happen?

sorry if i explained that badly, iv never been good at explaining things.

I am not positive, but it appears you are describing gravitational waves. Note there is no mention in the below descriptions of the term "fabric of space". Instead, find ripples or perturbations in the "curvature of spacetime".

“A gravitational-wave detector is any device designed to measure gravitational waves, minute distortions of spacetime that are predicted by Einstein's theory of general relativity. The existence of gravitational radiation is a prediction of general relativity. Gravitational waves are perturbations in the curvature of spacetime caused by accelerated masses.”http://en.wikipedia.org/wiki/Gravitational-wave_detector